scholarly journals Stability and Stability Degree of a Cracked Flexible Rotor Supported on Journal Bearings

1999 ◽  
Vol 122 (2) ◽  
pp. 116-125 ◽  
Author(s):  
G. Meng ◽  
R. Gasch
Keyword(s):  
Journal Bearings ◽  
Speed Ratio ◽  
Stiffness Ratio ◽  
Mass Ratio ◽  
Flexible Rotor ◽  
Cracked Rotor ◽  
Unstable Region ◽  
Stability Degree ◽  
Large Influence ◽  
The Stability

This paper investigates the stability and the stability degree of a cracked flexible rotor supported on different kinds of journal bearings. It is found that no matter what kinds of bearings are used, the unstable zones caused by rotor crack locate always within the speed ratio of 2/N1−ΔKξ /4<Ω<2/N when gravity parameter Wg>1.0; and locate always within the speed ratio of 2Ωα/N1−ΔKξ /4<Ω<2Ωα/N when Wg<0.1, where ΔKξ is the crack stiffness ratio, N=1,2,3,4,5,… and Ωα=1+1/2α1/2. When 0.1<Wg<1.0, there is a region where no unstable zones caused by rotor crack exist. Outside the crack ridge zones, the rotor crack has almost no influence on the system’s stability and stability degree; while within the crack ridge zones, the stability and the stability degree depend both on the crack and the system’s parameters. In some cases, the system may still be stable even though the crack is very large. For small gravity parameter Wg<0.1, the mass ratio α has a large influence on the position of the unstable region, but its influence on the stability degree is small. The influence of fixed Sommerfeld number So on the stability degree of the cracked rotor is small, although So has a large influence on the stability degree of the uncracked rotor. [S0739-3717(00)70502-2]

scholarly journals Stability and Stability Degree of a Cracked Flexible Rotor Supported on Journal Bearings

1993 ◽  
Author(s):  
Meng Guang ◽  
Robert Gasch
Keyword(s):  
Journal Bearings ◽  
Speed Ratio ◽  
Mass Ratio ◽  
Flexible Rotor ◽  
Cracked Rotor ◽  
Unstable Region ◽  
Stability Degree ◽  
Large Influence ◽  
Crack Stability ◽  
The Stability

Abstract This paper investigates the stability and the stability degree of a flexible cracked rotor supported on different kinds of journal bearings. It is found that no matter what kind of bearings is used, the unstable zones caused by rotor crack locate always within the speed ratio 2N(1-△Kξ4)&lt;Ω&lt;2N when gravity parameter Wg &gt; 1.0; and locate always within the speed ratio 2ΩαN(1-△Kξ4)&lt;Ω&lt;2ΩαN when Wg &lt; 0.1, where ΔKξ is the crack stiffness ratio, N = 1, 2, 3, 4, 5 … and Ωα=(1+2α2α)1/2. When 0.1 &lt; Wg &lt; 1.0, there is a region, where no unstable zones caused by rotor crack exist. Outside the crack ridge zones, the rotor crack has almost no influence on system’s stability and stability degree; while within the crack ridge zones, the stability and stability degree depend both on the crack and system’s parameters. In some cases, the system may still be stable even the crack is very large. For small gravity parameter (Wg &lt; 0.1), the mass ratio α has large influence on the position of unstable region, but its influence on the stability degree is small. The influence of fixed Sommerfeld number So on the crack stability degree is small although So has large influence on the stability degree of uncracked rotor.

Nonlinear Simulation Analysis and Experiment of Fluid Plain Journal Bearing With Incompressible Fluid

2003 ◽  
Author(s):  
Katsuhisa Fujita ◽  
Atsuhiko Shintani ◽  
Koji Yoshioka ◽  
Kouhei Okuno ◽  
Hiroaki Tanaka ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Incompressible Fluid ◽  
Journal Bearing ◽  
Simulation Analysis ◽  
Journal Bearings ◽  
Stable Region ◽  
Flexible Rotor ◽  
Nonlinear Simulation ◽  
Fluid Forces ◽  
The Stability

Recently, in many areas such as computers and information equipments etc., the fluid journal bearings are required to rotate at higher speed. To satisfy this requirement, the strictly stability analysis of the journal is indispensable. In this paper, we investigate the stability analysis of the dynamic behavior of the fluid plain journal bearing with an incompressible fluid considering the nonlinear terms of fluid forces. The stability analysis is examined by the numerical simulations on each model of a rigid rotor and a flexible rotor. The stable regions by nonlinear analysis are compared with the regions by classical linear analysis. Performing the nonlinear simulation analysis, it becomes clear that there is rather a stable region which amplitude does not grow up abruptly, and this phenomenon can not only be pointed out, but also is judged to be unstable by linear stable analysis. Finally, the experiment using actual bearings is performed and compared with the numerical results.

The Stability of a Flexible Rotor Supported by Circumferentially Fed Journal Bearings

1977 ◽  
Vol 99 (4) ◽  
pp. 469-477 ◽  
Author(s):  
P. Bar-Yoseph ◽  
J. J. Blech
Keyword(s):  
Journal Bearings ◽  
Asymptotically Stable ◽  
Direct Integration ◽  
Flexible Rotor ◽  
Nonlinear Prediction ◽  
Speed Range ◽  
The Stability

The stability of a flexible rotor, perfectly balanced, was investigated theoretically. The rotor is symmetrically supported by circumferentially fed journal bearings. Short and finite bearings were treated. Stability was checked for small and large disturbances. Two methods were employed to treat large disturbances: Direct integration and the slowly varying technique. The nonlinear prediction was tested concurrently with the prediction of the stability charts. It was observed that in certain cases stability can be obtained in the asymptotic and in the unstable regions. Instability was obtained for regions which presumably are asymptotically stable in the entire speed range.

The Stability of an Elastic Rotor in Journal Bearings With Flexible, Damped Supports

1965 ◽  
Vol 32 (4) ◽  
pp. 911-920 ◽  
Author(s):  
Jorgen W. Lund
Keyword(s):  
Theoretical Analysis ◽  
Dynamic Properties ◽  
Journal Bearings ◽  
Rotor Speed ◽  
Flexible Rotor ◽  
Damping Coefficients ◽  
Oil Whip ◽  
The Stability ◽  
Rotor Stiffness ◽  
Gas Bearing

A theoretical analysis is presented investigating the stability (fractional frequency whirl, “oil whip”) of a symmetrical, flexible rotor supported in journal bearings. The bearings are mounted in flexible, damped supports. The analysis determines the rotor speed at which instability sets in as affected by rotor stiffness, the dynamic properties of the bearing film, and the flexibility and damping of the bearing supports. The analysis is based on the fact that the bearing can be represented by frequency-dependent spring and damping coefficients, and the method by which the coefficients are obtained is described with emphasis on the gas-lubricated bearing. The conclusions are: (a) Rotor and support flexibility by themselves lower the speed at onset of instability; (b) when the bearing support possesses damping in addition to flexibility, the speed at onset of instability can be raised significantly above the threshold speed of a rotor in rigidly mounted bearings. Numerical results are presented in the form of graphs for the plain cylindrical gas bearing.

Experiments on the Stability and Response of a Flexible Rotor in Three Types of Journal Bearings

1982 ◽  
Vol 25 (3) ◽  
pp. 289-298 ◽  
Author(s):  
R. F. Lanes ◽  
R. D. Flack ◽  
D. W. Lewis
Keyword(s):  
Journal Bearings ◽  
Flexible Rotor ◽  
The Stability

On the Stability of the Linearly Related Modes of Certain Nonlinear Two-Degree-of-Freedom Systems

1961 ◽  
Vol 28 (1) ◽  
pp. 71-77 ◽  
Author(s):  
C. P. Atkinson
Keyword(s):  
Nonlinear Differential Equations ◽  
Mass Ratio ◽  
Positive Mass ◽  
Fourth Degree ◽  
Real Roots ◽  
General Stability ◽  
The Stability ◽  
The Masses ◽  
Spring Constants ◽  
Two Degree Of Freedom

This paper presents a method for analyzing a pair of coupled nonlinear differential equations of the Duffing type in order to determine whether linearly related modal oscillations of the system are possible. The system has two masses, a coupling spring and two anchor springs. For the systems studied, the anchor springs are symmetric but the masses are not. The method requires the solution of a polynomial of fourth degree which reduces to a quadratic because of the symmetric springs. The roots are a function of the spring constants. When a particular set of spring constants is chosen, roots can be found which are then used to set the necessary mass ratio for linear modal oscillations. Limits on the ranges of spring-constant ratios for real roots and positive-mass ratios are given. A general stability analysis is presented with expressions for the stability in terms of the spring constants and masses. Two specific examples are given.

Characteristics of Herringbone-Grooved, Gas-Lubricated Journal Bearings

1965 ◽  
Vol 87 (3) ◽  
pp. 568-576 ◽  
Author(s):  
J. H. Vohr ◽  
C. Y. Chow
Keyword(s):  
Differential Equation ◽  
Journal Bearing ◽  
Groove Depth ◽  
Radial Force ◽  
Journal Bearings ◽  
Speed Ratio ◽  
Plain Bearing ◽  
Relative Speed ◽  
Whirl Speed ◽  
Limiting Case

A differential equation is obtained for the smoothed “overall” pressure distribution around a herringbone-grooved, gas-lubricated journal bearing operating with a variable film thickness. The equation is based on the limiting case of an idealized bearing for which the number of grooves approaches an infinite number. A numerical solution to the differential equation is obtained valid for small eccentricities. This solution includes the case where the journal is undergoing steady circular whirl. In addition to the usual plain bearing parameters L/D, Λ, and whirl speed ratio ω3/(ω1 + ω2), the behavior of a grooved bearing also depends on four additional parameters: The groove angle β, the relative groove width α, the relative groove depth H0, and a compressibility number, Λs, which is based on the relative speed between the grooved and smooth members of the bearing. Results are presented showing bearing radial force and attitude angle as functions of β, α, H0, Λs, Λ, and whirl speed ratio.

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